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Suppose there are two full bowls of cookies. Bowl #1 has 13 chocolate chip and 22...

Suppose there are two full bowls of cookies. Bowl #1 has 13 chocolate chip and 22 plain cookies, while bowl #2 has 29 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. The cookie turns out to be a plain one. What is the probability that Fred picked Bowl #1?

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Answer #1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(Bowl #1 | Plain cookie) = P(Bowl #1 and plain cookie) / P(plain cookie)

= P(Bowl #1 and plain cookie)/[P(Bowl #1 and plain cookie) + P(Bowl #2 and plain cookie)]

= (0.5 x 22/35) / (0.5 x 22/35 + 0.5 x 29/58)

= 0.5570

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